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Golomb Rulers Roger C. Alperin

Summary: Golomb Rulers
Roger C. Alperin
San Jose State University
San Jose, CA 95192
Vladimir Drobot
Department of Computer Science
San Jose State University
San Jose, CA 95192
The Math Factor podcast posed the problem of finding the smallest num-
ber of inch marks on a 12 inch ruler so that one could still measure any integer
length from 1 to 12. One needs only four additional marks besides 0 and 12;
for example 1, 4, 7, 10 works. This entertaining problem lead to others dur-
ing the next few minutes (you can listen at mathfactor.uark.edu/2005/10)
and inspired us to look for generalizations. After several false starts and
numerous literature searches we uncovered the fascinating theory of Golomb
and minimal spanning rulers, a generalization to the natural numbers and
relations to an unsolved conjecture of Erd¨os and Turan.
We begin the discussion with our first problem--­ which led us to Golomb


Source: Alperin, Roger C. - Department of Mathematics, San Jose State University


Collections: Mathematics